We propose a class of the two Higgs doublet standard models (SMs) with a SM singlet and a class of supersymmetric SMs with two pairs of Higgs doublets, where the right-handed up/charm quarks and the right-handed top quark have different quantum numbers under extra discrete symmetries. Thus, the right-handed up and charm quarks couple to one Higgs doublet field, while the right-handed top quark couples to another Higgs doublet. The quark Cabibbo-Kobayashi-Maskawa mixings can be generated from the down-type quark sector. As one of the phenomenological consequences of our models, we explore whether one can accommodate the observed direct CP asymmetry difference in singly Cabibbo-suppressed D decays. We how that it is possible to explain the measured values of CP violation under relevant experimental constraints.